Scalar data processing method and apparatus

Description

BACKGROUND OF THE INVENTION

(1) Field of the Invention

[0001] The present invention relates to a scalar data processing apparatus and a method for compressing two-dimensional scalar data and for reconstructing the compressed two-dimensional scalar data.

[0002] It is desired to efficiently transmit and reconstruct two-dimensional scalar data φ (x,y) such as luminance data of a picture on a two-dimensional surface or concave-convex data of a relief formed on a wall surface, or to efficiently determine a two-dimensional function φ (x,y) of a curved surface of an object such as a car body when the outer shape of the object is to be determined.

(2) Description of the Related Art

[0003] Conventionally, to transmit and reconstruct two-dimensional scalar data, or to determine the two-dimensional function, data of each pixel on the picture surface or each point on the desired body is used. This, however, requires that a tremendous amount of data be processed.

[0004] Therefore, it,has been desired to enable the reconstruction of two-dimensional scalar data with a small amount of data, smaller than the number of pixels or points on the picture surface.

[0005] Reference can be made to U.S.Patent No. 4,908,698 issued on March 13, 1990, corresponding to Japanese Patent Applications Nos. 62-133690 and 63-39284, filed by the same assignee of the present inventors. These applications are directed to providing a color picture synthesis technique in which, in a color picture transmission, a chrominance component of a given picture is separated into a lamellar component and a vortex component for transmission, and a synthesis of the color picture in combination with a luminance component in the above given picture is effected. This technique can be utilized in the present invention.

[0006] In the above proposal, the chrominance component is expressed by a vector V, and when the Helmholtz theory is applied to the vector V, it is noted that the vector V can be expressed as:

   where L(x,y) is a scalar potential such as the luminance, and R · K is a vector potential having a direction expressed by a unit vector K in the direction of the Z axis.

[0007] The lamellar component is the first item, i.e., grad L, in the above expression (1), and the vortex component is the second item, i.e., rot (R · K), in the above expression (1). By detecting and transmitting an edge line of the chrominance component by detecting only divergence V and rotation V which exceed predetermined threshold values which are the values on the edge line of the chrominance component of the picture, the chrominance component of the color picture for every point can be reconstructed by interpolation.

[0008] In accordance with the Helmholtz theory, if a vector V does not have a vortex component, the vector V is expressed by only the lamellar component grad L. The gradient component of the two-dimensional scalar data φ such as luminance is a vector. Therefore, if the vector V can be expressed by a scalar potential grad φ, the Helmholtz theory is expressed as :

[0009] An edge line of the scalar data is determined as a place where the divergence and rotation of the vector are greatly changed. The divergence of the vector in the expression (2) is

The rotation of the vector V in the expression (2) is

As a result of the above expressions (3) and (4), to detect the edge line of scalar data, since the rotation of the gradient φ is always zero, the edge line of the scalar data φ can be determined by detecting only the divergence of the gradient φ, i.e., the Laplacian Δ φ, which exceeds the predetermined threshold value. Since the rotation of the vector V is always zero, it is not necessary to consider the rotation of the vector V. The Laplacian Δ φ, the absolute value of which exceeds the predetermined threshold value can be detected by detecting the value φ and its gradient on the edge line. The present invention makes use of these facts and incorporates the feature that once the value φ and its gradient on the edge line are given, the values φ at the other points can be estimated by interpolation because the values φ at the other points are changed smoothly.

[0010] A system for image coding and reconstruction is also disclosed in IEEE Transactions on circuits and systems, Volume CAS-34, November 1987, No. 11, pages 1306-1336, by M. Kunt, et al., entitled "Recent results in high compression image coding". The technique disclosed is based on contour-texture modelling two-dimensional approximation, directional decomposition, region growing, and split and merge operations. The technique of adaptive split and merge used in this prior art is based on adaptive segmentation, a split process, a merge process, information representation and coding, and postprocessing. The adaptive segmentation is based on a contour extraction technique from which are obtained a set of two-dimensional analytical functions which are made to approximate to the contours. The split process serves to define homogenous regions in the image which can be used as a basis for the remainder of the segmentation. The merge process leads to the fitting of the region boundaries to the contours of the objects in a scene contained in the image data. Once this step has been achieved, the region position and shape of each region is reconstructed in the information representation and coding step. Finally, the postprocessing serves to enhance the final image through the use of a smoothing algorithm.

SUMMARY OF THE INVENTION

[0011] The present invention has an object to enable a reduction in the amount of data in the transmission or storing of two-dimensional scalar data by compressing two-dimensional data by the boundary value on the edge lines and by applying an interpolation for reconstructing the compressed data.

[0012] According to the present invention, this object is achieved by a scalar data processing method for processing scalar information signal data, such as image signal data, by compressing two-dimensional scalar information signal data defined on a two-dimensional surface having a horizontal direction (i) and a vertical direction (j) and by reconstructing said two-dimensional scalar information signal data based on said compressed data, comprising the steps of :

1) detecting (at 51) edge lines (11-1, 11-2) of said two-dimensional scalar information signal data (φ(i, j)), said edge lines (11-1, 11-2) being detected in such a way that a change in the value of said two-dimensional scalar information signal data between adjacent points on said two-dimensional surface is larger than a predetermined threshold value;

2) cutting (at 532) a domain (12) between said edge lines (11-1, 11-2) along a first honzontal line (17) intersecting said edge lines;

3) determining (at 533) a function (f(i)) as an approximation of a Laplacian of said two-dimensional scalar data (φ(i, j)) calculated at each point in said cut domain (12) along said horizontal line;

4) compressing (at 534) said two-dimensional scalar information signal data (φ(i, j)) by replacing said two-dimensional scalar data at each of said points along said horizontal line (17) by scalar data at the intersection (13-1, 13-2) of said honzontal line with said edge lines (11-1, 11-2), scalar data representing gradients between said two-dimensional scalar data at said edge lines and adjacent points (14-1, 14-2) along said honzontal line, and said function (f(i));

5) repeating steps 2-4 along further horizontal lines in parallel with said first horizontal line (17); and

6) reconstructing (at 535) said two-dimensional scalar data by interpolating said two-dimensional scalar data based on said scalar data at said edge lines (11-1, 11-2), said scalar data representing gradients between said two-dimensional scalar data at said edge lines and adjacent points (14-1, 14-2) along said horizontal line, and said function (f(i)) obtained in said compressing step.

[0013] The scalar data processing apparatus according to the present invention comprises an apparatus for processing scalar information signal data, such as image signal data, by compressing two-dimensional scalar information signal data defined on a two-dimensional surface having a horizontal direction (i) and a vertical direction (j) and for reconstructing said two-dimensional scalar information signal data based on said compressed data, said apparatus comprising :

1) means (51) for detecting edge lines (11-1, 11-2) of said two-dimensional scalar information signal data (φ(i, j)), said edge lines (11-1, 11-2) being detected in such a way that a change in the value of said two-dimensional scalar information signal data between adjacent points on said two-dimensional surface is larger than a predetermined threshold value;

2) means (532) for cutting a domain (12) between said edge lines (11-1, 11-2) along a first horizontal line (17) intersecting said edge lines;

3) means (533) for determining a function (f(i)) as an approximation of a Laplacian of said two-dimensional scalar data (φ(i, j)) calculated at each point in said cut domain (12) along said horizontal line;

4) means (534) for compressing said two-dimensional scalar information signal data (φ(i, j)) by replacing said two-dimensional scalar data at each of said points along said horizontal line (17) by scalar data at the intersection (13-1, 13-2) of said horizontal line with said edge lines (11-1, 11-2), scalar data representing gradients between said two-dimensional scalar data at said edge lines and adjacent points (14-1, 14-2) along said horizontal line, and said function (f(i));

5) means for repeating steps 2-4 along further horizontal lines in parallel with said first horizontal line (17); and

6) means (535) for reconstructing said two-dimensional scalar data by interpolating said two-dimensional scalar data based on said scalar data at said edge lines (11-1, 11-2), said scalar data representing gradients between said two-dimensional scalar data at said edge lines and adjacent points (14-1, 14-2) along said honzontal line, and said function (f(i)) obtained in said compressing means.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] 

Figure 1 is a flowchart showing the principle operation of the scalar data processing according to an embodiment of the present invention;

Fig. 2A shows equations used for effecting interpolation according to an embodiment of the present invention;

Fig. 2B shows a display surface for explaining the interpolation process according to an embodiment of the present invention;

Fig. 3A shows a display surface for explaining the interpolation process according to another embodiment of the present invention;

Fig. 3B shows equations used for effecting interpolation in the embodiment shown in Fig. 3A;

Fig. 4 is a flowchart for explaining the total operation from the detection of the edge lines of the two-dimensional scalar data to the output of the two-dimensional scalar data, including the steps 2 to 4 in Fig. 1, according to an embodiment of the present invention; and

Fig. 5 is a block diagram showing a scalar data processing apparatus according to an embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] Figure 1 is a flowchart showing the principle operation of the scalar data processing according to an embodiment of the present invention. The right hand side of the flowchart represents a picture on a display 10.

[0016] In the right-hand side figure in Fig. 1, reference 10 represents a display in which "i" represents an x coordinate in the horizontal direction and "j" represents a y coordinate in the longitudinal direction, 11-1 and 11-2 represent the edge lines, 12 represents a domain cut by the edge lines 11-1 and 11-2, 13-1 and 13-2 represent points on the edge lines 11-1 and 11-2 and on the horizontal scanning line 17, 14-1 and 14-2 represent points on the horizontal scanning line 17 adjacent to the points 13-1 and 13-2 on the edge lines 11-1 and 11-2, 15 represents a point within the cut domain 12 which is the subject for the interpolation, 16-1, 16-2, 16-3, and 16-4 represent points adjacent to the point 15, and 17 represents a horizontal scanning line.

[0017] In the figure, reference 1 is a step for detecting boundaries 11-1 and 11-2 (referred to as edge lines) of two-dimensional scalar data such as luminance of a picture image when the picture image is the subject to be processed. The edge line detecting step 1 is carried out by utilizing appropriate means as disclosed in U.S.Patent No. 4,908,698 corresponding to Japanese Patent Application No. 63-39284, and therefore a practical explanation thereof is omitted here.

[0018] Reference 2 is a step for cutting the domain 12 on a horizontal line 17 between the edge lines 11-1 and 11-2 detected by the edge line detecting step 1.

[0019] Reference 3 is a step for determining a Laplacian Δ φ corresponding to the scalar data φ within the domain cut as above by approximating the Laplacian Δ φ to be a function f(i) with respect to the coordinate on the horizontal scanning line.
Namely,the Laplacian Δ φ is approximated as a function f(i) which may be a constant value including zero, a linear function of the coordinate i, a quadratic function of the coordinate i, or a three-dimensional function of the coordinate i, in accordance with the desired precision. In the Laplacian determining step 3, cooefficients in the function are determined by, for example, the method of least squares.

[0020] Reference 4 is a step for compressing data by extracting the values φ (i,j) on the edge lines 11-1 and 11-2, values φ (i,j) at points adjacent to the points on the edge lines 11-1 and 11-2 for providing values of grad φ (i,j) on the edge lines, and the above-mentioned function f(i) as the Laplacian Δ φ within the cut domain 12.

[0021] Reference 5 is a step of interpolation to obtain the values φ (i,j) of the respective points on the horizontal scanning line 17 and within the cut domain 12 to reconstruct the original two-dimensional scalar data φ .

[0022] In the domain cutting step 2, the edge lines 11-1 and 11-2 are shown on the display 10. A domain 12 on the horizontal scanning line 17 is cut by the edge lines 11-1 and 11-2.

[0023] In the Δ φ determining step 3, a Laplacian Δ φ is calculated at each point on each horizontal scanning line by the use of the values of the scalar data φ on the edge lines 11-1 and 11-2 and its gradient on the edge lines 11-1 and 11-2 and by the use of the scalar data φ in the cut domain 12. Within the cut domain 12, the change of the Laplacian Δ φ is considered to be smooth. Therefore, the Laplacian Δ φ can be approximated as a simple function f(i). Since there are four boundary values, i.e., the two scalar data on the edge lines and the two values of gradients on the edge lines, the function f(i) can be expressed by at maximum a three-dimensional function with respect to the coodinate value i on the horizontal scanning line.

[0024] Accordingly, as the above function f(i), the following function may be applied.

[0025] The constant value in the equation ( i ), the coefficients a and b in the equation ( ii ), the coefficients a, b, and c in the equation ( iii ), or the coefficients a, b, c, and d are determined in such a way that the function f(i) is as close as possible to the calculated Laplacian Δ φ at each point by, for example, means of the method of least squares. According to an experiment performed by the inventors, even when an approximation is taken so that

the reconstructed two-dimensional scalar data is sufficient to be used in practice.

[0026] When a higher degree of approximation is required, an approximation of higher accuracy is carried out by the use of the equation ( i ), ( ii ), ( iii ) or ( iv ).

[0027] In the data compression step 4, for each horizontal scanning line 17, the values φ (i,j) at the points 13-1 and 13-2 on the edge lines 11-1 and 11-2, the values φ (i,j) at the points 14-1 and 14-2 adjacent to the points 13-1 and 13-2 for calculating the gradients on the edge lines 11-1 and 11-2, and the above-mentioned function f(i) are used as compressed data. The compressed data is transmitted to a receiving side or is stored for reconstruction. Of course, the adjacent points 14-1 and 14-2 for obtaining the gradients on the edge lines are not restricted to two, but adjacent points on the edge lines 11-1 and 11-2 may also be taken into account. The values φ (i,j) and their gradients on the edge lines, however, do not greatly change in general. Therefore, it is sufficient to take into account only the above-mentioned two points 14-1 and 14-2 to obtain the gradient on the edge lines.

[0028] In the interpolation step 5, the value φ (i,j) at each point within the cut domain 12 on the horizontal scanning line 17 is obtained by interpolation to reconstruct the original two-dimensional scalar data. Namely, to obtain the value φ (i,j) at each point 15 within the domain 12, interpolation is carried out in accordance with a successive approximation by the use of the compressed data, i.e., the boundary values φ (i,j) on the edge lines 11-1 and 11-2, the boundary values grad φ (i,j) on the edge lines 11-1 and 11-2, and the above-mentioned function f(i).

[0029] According to the successive approximation used to obtain the value φ (i,j) at a point 15 within the cut domain 12, roughly determined values φ (i,j) at points 16-1, 16-2, 16-3, and 16-4 adjacent to the point 15 and a roughly determined value φ (i,j) at the point 15 are utilized to calculate a rough Laplacian Δ φ (i,j). The interpolation process is carried out in such a way that the above-mentioned function f(i) is satisfied as much as possible.

[0030] Figure 2A shows equations for carrying out the interpolation process according to an embodiment of the present invention, and Fig. 2B shows a display for explaining the interpolation process.

[0031] As shown in Fig. 2A, the equation (A), i.e., Δ φ = f(i), and the equation (B), i.e., Δ φ _k = φ _k (i+1,j)+ φ _k (i,j+1)+ φ _k (i-1,j)+ φ _k (i,j-1)-4 φ _k (i,j), where the suffix k represents the number of times of estimation, are utilized for interpolation.

[0032] Generally, the Laplacian Δ φ can be expressed by the equation (B) shown in Fig. 2A. This equation can be understood from the following calculations.





Similarly,

Accordingly,

[0033] First, based on the compressed data, the values φ (i,j) at the points 13-1 to 13-6 on the edge lines 11-1 and 11-2 are known. Also, the values φ (i,j) at the points 14-1 to 14-6 adjacent to the points 13-1 to 13-6 are known because the gradient φ (i,j) on the edge lines are included in the compressed data. Based on these values φ (i,j) at the points 13-1 to 13-6 and the values φ (i,j) at the points 14-1 to 14-6, the value at each point within the cut domain 12 is roughly estimated. For example, the first estimation is carried out in such a way that the values of the points between the points 14-1 and 14-2 are assumed to be linearly changed. By this estimation, it is assumed that the estimated value at each point within the cut domains 12-1 to 12-3 is expressed as φ ₁(i,j). Then, the estimated Laplacian Δ φ ₁(i,j) is calculated in accordance with the equation (B), where k=1.

[0034] Next, the estimated Laplacian △ φ ₁(i,j) and the function f(i) are compared to determine whether the estimated value △ φ ₁(i,j) satisfies the function f(i) . To this end, an error E₁ is calculated, where

[0035] When the absolute value of the error E₁ is larger than a predetermined threshold value, the first estimated values φ ₁(i,j) at each point are corrected to secondary estimated values φ ₂(i,j) in the following manner.

[0036] By using the secondary estimated values, a similar calculation is made according to the equation (B), i.e., Δ φ ₂(i,j) = φ ₂(i+1,j)+ φ ₂(i,j+1)+ φ ₂(i-1,j)+ φ ₂(i,j-1)-4 φ ₂(i,j). Then, if an error E₂ = f(i)-Δ φ ₂(i,j) is larger than the predetermined threshold value, the secondary estimated values φ ₂(i,j) at each point are corrected to third estimated values in a way similar to the above. Namely, by using the above relation, the correction is made and the value φ (i,j) at each point within the cut domain is converged so that the above-mentioned function f(i) is satisfied within the predetermined threshold value. As a result, the value φ (i,j) at each point on the two-dimensional surface can be reconstructed.

[0037] Figure 3A shows a display for explaining the interpolation process according to another embodiment of the present invention. In the illustrated case, the Laplacian Δ φ can also be expressed by the equation (D) shown in Fig. 3B. This equation can be undersood by the following calculations.





Similarly,

Accordingly,

[0038] First, based on the compressed data, the values φ (i,j) at the points 13-1 to 13-6 on the edge lines 11-1 and 11-2 are known. Also, the values φ (i,j) at the points 14-1 to 14-6 adjacent to the points 13-1 to 13-6 are known as explained before. Based on these values φ (i,j) at the points 13-1 to 13-6 and the values φ (i,j) at the points 14-1 to 14-6, the value at each point within the cut domain is roughly estimated in the same way as described with reference to Fig. 2B. By this estimation, it is assumed that the estimated value at each point within the cut domains 12-1 to 12-3 is expressed as φ ₁(i,j). Then, the estimated Laplacian Δ φ ₁(i,j) is calculated in accordance with the equation (D).

[0039] Next, the estimated Laplacian Δ φ ₁(i,j) and the function f(i) are compared to determine whether the estimated value Δ φ ₁(i,j) satisfies the function f(i) To this end, an error E₁ is calculated, where

[0040] When the absolute value of the error E₁ is larger than a predetermined threshold value, the first estimated value φ ₁(i,j) at each point is corrected to a secondary estimated value φ ₂(i,j) in the following manner.

[0041] By using the secondary estimated values, a similar calculation is carried out according to the equation (D), i.e., Δ φ ₂(i,j) = 2 φ ₂(i,j)- 2 φ ₂(i-1,j) + φ ₂(i-1,j)-2 φ ₂(i,j-1)+ φ ₂(i,j-2). Then, if an error E₂ = f(i)- Δ φ ₂(i,j) is greater than the predetermined threshold value, the secondary estimated value φ ₂(i,j) at each point is corrected to a third estimated value in the similar way as above. Namely, by using the above relation, the correction is made and the value φ (i,j) at each point within the cut domain is converged so that the above-mentioned function f(i) is satisfied within the predetermined threshold value.

[0042] Figure 4 is a flowchart for explaining the total operation from the detection of the edge lines of the two-dimensional scalar data to the output of the two-dimensional scalar data, including the steps 2 to 4 in Fig. 1, according to an embodiment of the present invention.

[0043] In the figure, reference 100 represents a basic process including the steps 2 to 4 shown in Fig. 1, 1 represents a edge line detecting step, 101 represents a storing step for storing edge line data before correction, 102 represents a total display process, 103 represents a precision or naturality judging process, 104 represents a step for extracting portions where the precision or naturality is insufficient, 105 represents a step for providing edge lines for expanding the structure of the two-dimensional scalar data, and 106 represents a step for forming data of new edge lines.

[0044] Before carrying out the basic process 100, the edge lines are detected by the edge line detecting step 1 illustrated in Fig. 1, and the detected edge lines are stored in a memory (not shown) in the step 101.

[0045] In the basic process 100, the data of the detected edge lines are processed in the steps 2 to 4 according to the method described before so that the two-dimensional scalar data similar to the original two-dimensional scalar data is reconstructed. The reconstructed two-dimensional scalar data is displayed on, for example, a display surface in the total display process 102.

[0046] In the precision or naturality judging process 103, in view of the illustrated picture image of the two-dimensional scalar data, an operator, for example, checks to determine whether there is an insufficiency in the precision or in the naturality. The precision is judged when the compressed data of the two-dimensional scalar data is to be transmitted. The naturality is judged when the two-dimensional scalar data is given by, for example a car designer, and when compressed data of the two-dimensional scalar data is to be stored. If there is an insufficiency, that portion is extracted in the step 104 for extracting a portion where the precision or the naturality is insufficient. Such a portion is, for example, a portion where the change of the luminance is comparatively smooth so that no edge line is found, causing the above-mentioned insufficiency.

[0047] In the step 105 for providing edge lines for expanding the structure, data of a new edge line corresponding to the above-mentioned insufficient portion is provided. Then, in step 106, the data of the new edge line is combined with the data of the edge lines stored in the step 101 before correction so that data of a new edge line is obtained. The data of the new edge line is introduced to the basic process 100 so that the two-dimensional scalar data is again reconstructed.

[0048] These new edge lines play a role to correct values of φ (i,j) to satisfy the designer. In this case, these new edge lines give correction lines which are virtual lines.

[0049] The above-mentioned steps 100 to 106 are repeated until data having sufficient precision or sufficient naturality is obtained. If the reconstructed data is sufficient, it is output.

[0050] Figure 5 is a block diagram showing a scalar data processing apparatus according to an embodiment of the present invention. In the figure, 51 represents a edge line detecting unit, 52 represents a edge line data storing memory for storing edge line data before correction, and 53 represents a basic process unit including a domain cutting unit 532, a Δ φ determining unit 533, a data compressing unit 534, and an interpolation unit 535. Reference 54 is a display for effecting a total display process, 55 represents a precision or naturality judging unit, 56 represents a unit for extracting portions where the precision or naturality is insufficient, 57 represents a unit for providing edge lines for expanding the structure of the two-dimensional scalar data, and 58 represents a unit for forming data of new edge lines.

[0051] The operation of the scalar data processing apparatus shown in Fig. 5 is already described with reference to Fig. 4.

[0052] In the present invention, the following windows are provided so that display is carried out by a multi-window system in accordance with necessity. Namely, there are provided:

( i ) an edge line display window

( ii ) an edge line circumferential data display window

( iii ) a data display window

( iv ) a texture definition/superimposition display window

( v ) a new edge line display window

( vi ) a process history display window and

( vii ) a moving picture/animation display window.

[0053] The above windows ( i ), ( ii ), and ( iii ) are used to extract the values φ (i,j) and their gradients on the edge lines. The window ( iv ) is used to compensate the parts where the above-mentioned compression and interpolation process are insufficient to obtain the desired reconstructed scalar data. The window ( v ) is used in the step 106 shown in Fig. 4. The windows ( vi ) and ( vii ) are used in the steps 100 to 106 in accordance with necessity.

[0054] Also, as window operating functions, the following functions are provided. Namely, there are provided:

( i ) edge line definition/correction function

( ii ) data definition/correction function

( iii ) definition of interpolation data output display-structure expansion edge line/correction function

( iv ) texture definition/correction function

( v ) definition of continuousness of a moving picture/correction function and

( vi ) texture definition in a domain/correction function.

[0055] From the foregoing description, it is apparent that, according to the present invention, the data value φ (i,j) of two-dimensional scalar data at each point can be reconstructed in such a way that

becomes within a threshold value. Namely, by transmitting the function f(i) and, for example, the data values φ (i,j) of at least four points on the edge lines and adjacent to the edge lines, the original two-dimensional scalar data can be reconstructed.

[0056] The present invention can be applied not only when the two-dimensional scalar data is to be transmitted but also when the two-dimensional scalar data is to be stored by, for example, a car designer.

Claims

1. A method of processing scalar information signal data, such as image signal data, by compressing two-dimensional scalar information signal data defined on a two-dimensional surface having a horizontal direction (i) and a vertical direction (j) and of reconstructing said two-dimensional scalar information signal data based on said compressed data, comprising the steps of:

1) detecting (at 51) edge lines (11-1, 11-2) of said two-dimensional scalar information signal data (φ(i, j)), said edge lines (11-1, 11-2) being detected in such a way that a change in the value of said two-dimensional scalar information signal data between adjacent points on said two-dimensional surface is larger than a predetermined threshold value;

2) cutting (at 532) a domain (12) between said edge lines (11-1, 11-2) along a first horizontal line (17) intersecting said edge lines;

3) determining (at 533) a function (f(i)) as an approximation of a Laplacian of said two-dimensional scalar data (φ(i, j)) calculated at each point in said cut domain (12) along said horizontal line;

4) compressing (at 534) said two-dimensional scalar information signal data (φ(i, j)) by replacing said two-dimensional scalar data at each of said points along said horizontal line (17) by scalar data at the intersection (13-1, 13-2) of said horizontal line with said edge lines (11-1, 11-2), scalar data representing gradients between said two-dimensional scalar data at said edge lines and adjacent points (14-1, 14-2) along said horizontal line, and said function (f(i));

5) repeating steps 2-4 along further horizontal lines in parallel with said first horizontal line (17); and

6) reconstructing (at 535) said two-dimensional scalar data by interpolating said two-dimensional scalar data based on said scalar data at said edge lines (11-1, 11-2), said scalar data representing gradients between said two-dimensional scalar data at said edge lines and adjacent points (14-1, 14-2) along said horizontal line, and said function (f(i)) obtained in said compressing step.

2. A scalar data processing method as claimed in claim 1, wherein in said step (at 533) for determining a function (f(i)), the function is assumed as zero.

3. A scalar data processing method as claimed in claim 1, wherein in said step (at 533) for determining a function (f(i)), the function is assumed as a constant value different from zero.

4. A scalar data processing method as claimed in claim 1, wherein in said step (at 533) for determining a function (f(i)), the function is assumed as a linear function with respect to a coordinate of said horizontal line.

5. A scalar data processing method as claimed in claim 1, wherein in said step (at 533) for determining a function (f(i)), the function is assumed as a secondary order function with respect to a coordinate of said horizontal line.

6. A scalar data processing method as claimed in claim 1, wherein in said step (at 533) for determining a function (f(i)), the function is assumed as a third order function with respect to a coordinate of said horizontal line.

7. A scalar data processing method as claimed in claim 1, wherein in said step (at 533) for determining a function (f(i)), the function is determined by the method of least-square approximation with respect to the function and the Laplacian of said two-dimensional scalar data at each point on said two-dimensional surface.

8. A scalar data processing method as claimed in claim 1, wherein after said step (at 534) for compressing said two-dimensional scalar data (φ(i, j)), said replaced data is transmitted from a transmitting side to a receiving side when said two-dimensional scalar data is to be transmitted.

9. A scalar data processing method as claimed in claim 1, wherein after said step (at 534) for compressing said two-dimensional scalar data (φ(i, j)), said replaced data is transmitted from a transmitting side to a receiving side, and said step for interpolation is carried out at said receiving side.

10. A scalar data processing method as claimed in claim 1, wherein after said step (at 534) for compressing said two-dimensional scalar data (φ(i, j)), said replaced data are stored for reconstructing the original two-dimensional scalar data by said interpolation step.

11. A scalar data processing method as claimed in claim 1, wherein in said step (at 535) for reconstructing said two-dimensional scalar data, said interpolation is carried out by successive approximation in such a way that, at a first approximation, the approximated two-dimensional scalar data are determined based on the values of said edge lines and the values which represent the gradients of said two-dimensional scalar data, and then the estimated Laplacian (Δφ_K(i,j)) is calculated and compared with said function (f(i)) to determine whether the difference between said function and said estimated Laplacian (Δφ _K(i, j)) at each point comes within a predetermined threshold value, and if not, performing further similar approximations on the basis of corrected values unitl said difference (E_K) is within said threshold value.

12. A scalar data processing method as claimed in claim 11, wherein in said step (at 535) for reconstructing said two-dimensional scalar data, said value (Δφ_K(i, j)) of a Laplacian at each point is expressed as Δφ_K (i, j) = φ_K (i+1,j) + φ_K (i,j+1) + φ_K(i-1,j) + φ_K(i,j-1) - 4φ_K(i,j), where i is an x coordinate, j is a y coordinate, and k is the number of successive approximations.

13. A scalar data processing method as claimed in claim 11, wherein in said step (at 535) for reconstructing said two-dimensional scalar data. said value (Δφ_K(i,j)) of a Laplacian at each point is expressed as Δφ_K(i,j) = 2φ_K(i,j) - 2φ_K(i-1,j) + φ_K(i-2,j) - 2φ_K(i,j-1) + φ_K(i,j-2), where i is an x coordinate, j is a y coordinate, and k is the number of successive approximations.

14. An apparatus for processing scalar information signal data, such as image signal data, by compressing two-dimensional scalar information signal data defined on a two-dimensional surface having a horizontal direction (i) and a vertical direction (j) and for reconstructing said two-dimensional scalar information signal data based on said compressed data, said apparatus comprising :

1) means (51) for detecting edge lines (11-1, 11-2) of said two-dimensional scalar information signal data (φ(i, j)), said edge lines (11-1, 11-2) being detected in such a way that a change in the value of said two-dimensional scalar information signal data between adjacent points on said two-dimensional surface is larger than a predetermined threshold value;

2) means (532) for cutting a domain (12) between said edge lines (11-1, 11-2) along a first horizontal line (17) intersecting said edge lines;

3) means (533) for determining a function (f(i)) as an approximation of a Laplacian of said two-dimensional scalar data (φ(i, j)) calculated at each point in said cut domain (12) along said horizontal line;

4) means (534) for compressing said two-dimensional scalar information signal data (φ(i, j)) by replacing said two-dimensional scalar data at each of said points along said horizontal line (17) by scalar data at the intersection (13-1, 13-2) of said horizontal line with said edge lines (11-1, 11-2), scalar data representing gradients between said two-dimensional scalar data at said edge lines and adjacent points (14-1, 14-2) along said horizontal line, and said function (f(i));

5) means for repeating steps 2-4 along further horizontal lines in parallel with said first horizontal line (17); and

6) means (535) for reconstructing said two-dimensional scalar data by interpolating said two-dimensional scalar data based on said scalar data at said edge lines (11-1, 11-2), said scalar data representing gradients between said two-dimensional scalar data at said edge lines and adjacent points (14-1, 14-2) along said horizontal line, and said function (f(i)) obtained in said compressing step.

Ansprüche

1. Verfahren zum Verarbeiten von Skalar-Information-Signaldaten wie beispielsweise Bildsignaldaten durch Verdichten von zweidimensionalen Skalarinformation-Signaldaten, die in einer zweidimensionalen Fläche mit einer horizontalen Richtung (i) und einer vertikalen Richtung (j) definiert sind, und zum Rekonstruieren der zweidimensionalen Skalarinformation-Signaldaten basierend auf den verdichteten Daten, mit den folgenden Schritten:

1) Detektieren (bei 51) von Kanten-oder Randlinien (11-1, 11-2) der zweidimensionalen Skalarinformation-Signaldaten (φ(i,j), wobei die Kanten-oder Randlinien (11-1, 11-2) in einer solchen Weise detektiert werden, daß eine Änderung in dem Wert der zweidimensionalen Skalarinformation-Signaldaten zwischen benachbarten Punkten auf der zweidimensionalen Fläche größer ist als ein vorherbestimmter Schwellenwert;

2) Schneiden (bei 532) einer Domäne (12) zwischen den Kanten-oder Randlinien (11-1, 11-2) entlang einer ersten horizontalen Linie (17), welche die Kanten-oder Randlinien schneidet;

3) Bestimmen (bei 533) einer Funktion (f(i)) als eine Annäherung einer Laplace'schen Größe der zweidimensionalen Skalar-Daten (φ(i,j), die bei jedem Punkt in der geschnittenen Domäne (12) entlang der horizontalen Linie berechnet wurden;

4) Verdichten (bei 534) der zweidimensionalen Skalarinformation-Signaldaten (φ(i,j) durch Ersetzen der zweidimensionalen Skalar-Daten bei jedem der Punkte entlang der horizontalen Linie (17) durch Skalar-Daten an der Schnittstelle (13-1, 13-2) der horizontalen Linie mit den Kanten-oder Randlinien (11-1, 11-2), wobei die Skalar-Daten Gradienten zwischen den zweidimensionalen Skalar-Daten an den Kanten-oder Randlinien und den benachbarten Punkten (14-1, 14-2) entlang der horizontalen Linie, und der Funktion (f(i)) wiedergeben;

5) Wiederholen der Schritte 2-4 entlang den horizontalen Linien, die parallel zu der ersten horizontalen Linie (17) sind; und

6) Rekonstruieren (bei 535) der zweidimensionalen Skalar-Daten durch Interpolieren der zweidimensionalen Skalar-Daten basierend auf den Skalar-Daten bei den Kanten-oder Randlinien (11-1, 11-2), wobei die Skalar-Daten Gradienten zwischen den zweidimensionalen Skalar-Daten an den Kanten- oder Randlinien und den benachbarten Punkten (14-1, 14-2) entlang der horizontalen Linie, und die Funktion (f(i)), die bei dem Verdichtungsschritt erhalten wurde, wiedergeben.

2. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem bei dem Schritt (bei 533) zum Bestimmen einer Funktion (f(i)), die Funktion als Null angenommen wird.

3. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem bei dem Schritt (bei 533) zum Bestimmen einer Funktion (f(i)) die Funktion als ein von Null verschiedener konstanter Wert angenommen wird.

4. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem bei dem Schritt (bei 533) zum Bestimmen einer Funktion (f(i)) die Funktion als eine lineare Funktion in bezug zu einer Koordinate der horizontalen Linie angenommen wird.

5. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem bei dem Schritt (bei 533) zum Bestimmen einer Funktion (f(i)) die Funktion als eine Funktion sekundärer Ordnung in bezug auf eine Koordinate der horizontalen Linie angenommen wird.

6. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem bei dem Schritt (bei 533) zum Bestimmen einer Funktion (f(i)) die Funktion als eine Funktion dritter Ordnung in bezug auf eine Koordinate der horizontalen Linie angenommen wird.

7. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem bei dem Schritt (bei 533) zum Bestimmen einer Funktion (f(i)) die Funktion durch das Verfahren der mittleren quadratischen Approximiation in bezug auf die Funktion und die Laplace'sche Größe der zweidimensionalen Skalar-Daten an jedem Punkt auf der zweidimensionalen Fläche bestimmt wird.

8. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem nach dem Schritt (bei 534) zum Verdichten der zweidimensionalen Skalar-Daten (φ(i,j)) die ersetzten Daten von der Sendeseite zu einer Empfangsseite übertragen oder gesendet werden, wenn die zweidimensionalen Skalar-Daten zu übertragen oder zu senden sind.

9. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem nach dem Schritt (bei 534) zum Verdichten der zweidimensionalen Skalar-Daten (φ(i,j)) die ersetzten Daten von einer Sendeseite zu einer Empfangsseite gesendet oder übertragen werden und bei dem der Schritt einer Interpolation bei der Empfangsseite ausgeführt wird.

10. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem nach dem Schritt (bei 534) zum Verdichten der zweidimensionalen Skalar-Daten (φ(i,j)) die ersetzten Daten für die Rekonstruktion der originalen zweidimensionalen Skalar-Daten durch den Interpolationsschritt gespeichert werden.

11. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 1, bei dem bei dem Schritt (bei 535) zum rekonstruieren der zweidimensionalen Skalar-Daten die Interpolation durch suksessive Annäherung in einer solchen Weise ausgeführt wird, daß bei einer ersten Annäherung die angenäherten zweidimensionalen Skalar-Daten auf den Werten der Kanten-oder Randlinien und den Werten, welche die Gradienten der zweidimensionalen Skalar-Daten wiedergeben, bestimmt werden, und dann die geschätzte Laplace'sche Größe (ΔΦ_K(i,j)) berechnet wird und mit der Funktion (f(i)) verglichen wird, um zu bestimmen, ob die Differenz zwischen der Funktion und der geschätzten Laplace'schen Größe (Δφ_K(i,j))bei jedem Punkt innerhalb eines vorherbestimmten Schwellenwertes liegt und, wenn dies nicht der Fall ist, weitere ähnliche Annäherungen auf der Grundlage der korrigierten Werte durchgeführt werden, bis die Differenz (E_K) innerhalb des Schwellenwertes liegt.

12. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 11, bei dem bei dem Schritt (bei 535) zum Rekonstruieren der zweidimensionalen Skalar-Daten der Wert (Δφ_K(i,j)) einer Laplace'schen Größe bei jedem Punkt ausgedrückt wird als Δφ_K(i,j) =φ_K(i,l,j) +φ_K(i,j+1) +φ_K(i-1,j) +φ_K(i,j-l)-4φ_K(i,j), worin 1 eine x Koordinate ist, j eine y Koordinate ist und k die Zahl der suksessiven Annäherungen ist.

13. Skalar-Daten-Verarbeitungsverfahren nach Anspruch 11, bei dem bei dem Schritt (bei 535) zum Rekonstruieren der zweidimensionalen Skalar-Daten der Wert (Δφ_K(i,j)) einer Laplace'schen Größe bei jedem Punkt ausgedrückt wird als Δφ_K(i,j)=2φ_K(i,j)-2φ_K(i-1,j)-2φ_K(i,j-1)+φ_K(i,j-2), worin i eine x Koordinate ist, j eine y Koordinate ist und k die Zahl der aufeinanderfolgenden Annäherungen angibt.

14. Gerät zum Verarbeiten von Skalarinformation-Signaldaten wie Bildsignaldaten durch Verdichten von zweidimensionalen Skalarinformation-Signaldaten, die auf einer zweidimensionalen Fläche definiert sind mit einer horizontalen Richtung (i) und einer vertikalen Richtung (j) und zum Rekonstruieren der zweidimensionalen Skalarinformation-Signaldaten basierend auf den verdichteten Daten, wobei das Gerät folgendes aufweist:

1) eine Einrichtung (51) zum Detektieren von Kanten-oder Randlinien (11-1, 11-2) der zweidimensionalen Skalarinformation-Signaldaten (φ(i,j)), wobei die Kanten-oder Randlinien (11-1, 11-2) in einer solchen Weise detektiert werden, daß eine Änderung in dem Wert der zweidimensionalen SkalarInformation-Signaldaten zwischen benachbarten Punkten auf der zweidimensionalen Fläche größer ist als ein vorherbestimmter Schwellenwert;

2) eine Einrichtung (532) zum Schneiden Eier Domäne (12) zwischen den Kanten-oder Randlinien (11-1,11-2) entlang einer ersten horizontalen Linie (17), welche die Kanten-oder Randlinien schneidet;

3) eine Einrichtung (533) zum Bestimmen einer Funktion (f(i)) als eine Annäherung einer Laplce'schen Größe der zweidimensionalen Skalar-Daten (φ(i,j)), die bei jedem Punkt in der geschnittenen Domäne (12) entlang der horizontalen Linie berechnet werden;

4) eine Einrichtung (534) zum Verdichten der zweidimensionalen Skalarinformation-Signaldaten (φ(i,j)) durch Ersetzen der zweidimensionalen Skalar-Daten bei jedem der Punkte entlang der horizontalen Linie (17) durch Skalar-Daten an der Schnittstelle (13-1, 13-2) der horizontalen Linie mit den Kanten-oder Randlinien (11-1, 11-2), wobei die Skalar-Daten Gradienten zwischen den zweidimensionalen Skalar-Daten an den Kanten-oder Randlinien und den benachbarten Punkten (14-1, 14-2) entlang der horizontalen Linie, und die Funktion (f(i))wiedergeben;

5) eine Einrichtung zum Wiederholen der Schritte 2-4 entlang weiterer horizontaler Linien, die parallel zu der ersten horizontalen Linie (17) sind; und

6) eine Einrichtung (535) zum rekonstruieren der zweidimensionalen Skalar-Daten durch Interpolieren der zweidimensionalen Skalar-Daten basierend auf den Skalar-Daten an den Kanten-oder Randlinien (11-1, 11-2), wobei die Skalar-Daten Gradienten zwischen den zweidimensionalen Skalar-Daten an den Kanten-oder Randlinien und den benachbarten Punkten (14-1, 14-2) entlang der horizontalen Linie, und die Funktion (f(i)), die bei dem Verdichtungsschritt erhalten wurde, wiedergeben.

Revendications

1. Procédé de traitement de données scalaires de signaux d'informations, telles que des données de signaux d'images, par compression de données scalaires bidimensionnelles de signaux d'informations définies sur une surface bidimensionnelle ayant une direction horizontale (i) et une direction verticale (j) et par reconstitution desdites données scalaires bidimensionnelles de signaux d'informations sur la base desdites données comprimées, le procédé comprenant les opérations suivantes :

1) détecter (en 51) des lignes frontières (11-1, 11-2) desdites données scalaires bidimensionnelles de signaux d'informations (φ(i,j)), lesdites lignes frontières (11-1, 11-2) étant détectées de telle manière qu'un changement de la valeur desdites données scalaires bidimensionnelles de signaux d'informations entre des points adjacents de ladite surface bidimensionnelle soit supérieur à une valeur de seuil prédéterminée ;

2) découper (en 532) un domaine (12) entre lesdites lignes frontières (11-1, 11-2) suivant une première ligne horizontale (17) ayant des intersections avec lesdites lignes frontières ;

3) déterminer (en 533) une fonction (f(i)) au titre d'une approximation du Laplacien desdites données scalaires bidimensionnelles (φ(i,j)), calculé en chaque point dudit domaine découpé (12) suivant ladite ligne horizontale ;

4) comprimer (en 534) lesdites données scalaires bidimensionnelles de signaux d'informations (φ(i,j)) en remplaçant lesdites données scalaires bidimensionnelles présentes en chacun desdits points suivant ladite ligne horizontale (17) par des données scalaires présentes aux intersections (13-1, 13-2) de ladite ligne horizontale avec lesdites lignes frontières (11-1, 11-2), les données scalaires représentant des gradients entre lesdites données scalaires bidimensionnelles présentes sur lesdites lignes frontières et des points adjacents (14-1, 14-2) suivant ladite ligne horizontale, et ladite fonction (f(i));

5) répéter les opérations 2 à 4 suivant d'autres lignes horizontales parallèles à ladite première ligne horizontale (17); et

6) reconstituer (en 535) lesdites données scalaires bidimensionnelles en interpolant lesdites données scalaires bidimensionnelles sur la base desdites données scalaires présentes sur lesdites lignes frontières (11-1, 11-2), lesdites données scalaires représentant des gradients entre lesdites données scalaires bidimensionnelles présentes sur lesdites lignes frontières et des points adjacents (14-1, 14-2) suivant ladite ligne horizontale, et ladite fonction (f(i)) obtenue au cours de ladite opération de compression.

2. Procédé de traitement de données scalaires selon la revendication 1, où, dans ladite opération (en 533) servant à déterminer une fonction (f(i), la fonction est supposée être zéro.

3. Procédé de traitement de données scalaires selon la revendication 1, où, dans ladite opération (en 533) servant à déterminer une fonction (f(i), la fonction est supposée être une valeur constante différente de zéro.

4. Procédé de traitement de données scalaires selon la revendication 1, où, dans ladite opération (en 533) servant à déterminer une fonction (f(i), la fonction est supposée être une fonction linéaire par rapport à la coordonnée de ladite ligne horizontale.

5. Procédé de traitement de données scalaires selon la revendication 1, où, dans ladite opération (en 533) servant à déterminer une fonction (f(i), la fonction est supposée être une fonction du deuxième degré par rapport à la coordonnée de ladite ligne horizontale.

6. Procédé de traitement de données scalaires selon la revendication 1, où, dans ladite opération (en 533) servant à déterminer une fonction (f(i), la fonction est supposée être une fonction du troisième degré par rapport à la coordonnée de ladite ligne horizontale.

7. Procédé de traitement de données scalaires selon la revendication 1, où, dans ladite opération (en 533) servant à déterminer une fonction (f(i)), la fonction est déterminée par la méthode d'approximation des moindres carrés relativement à la fonction et au Laplacien desdites données scalaires bidimensionnelles pour chaque point de ladite surface bidimensionnelle.

8. Procédé de traitement de données scalaires selon la revendication 1, où, après ladite opération (en 534) de compression desdites données scalaires bidimensionnelles (φ(i,j)), lesdites données remplacées sont transmises d'un côté d'émission à un côté de réception lorsque lesdites données scalaires bidimensionnelles doivent être transmises.

9. Procédé de traitement de données scalaires selon la revendication 1, où, après ladite opération (en 534) servant à comprimer lesdites données scalaires bidimensionnelles (φ(i,j)), les données remplacées sont transmises d'un côté d'émission à un côté de réception, et ladite opération d'interpolation est effectuée dudit côté de réception.

10. Procédé de traitement de données scalaires selon la revendication 1, où, après ladite opération (en 534) servant à comprimer lesdites données scalaires bidimensionnelles (φ(i,j)), lesdites données remplacées sont stockées en vue de la reconstitution des données scalaires bidimensionnelles initiales par ladite opération d'interpolation.

11. Procédé de traitement de données scalaires selon la revendication 1, où, dans ladite opération (en 535) servant à reconstituer lesdites données scalaires bidimensionnelles, ladite interpolation est effectuée par approximations successives de telle manière que, en une première approximation, les données scalaires bidimensionnelles approchées soient déterminées sur la base des valeurs desdites lignes frontières et des valeurs qui représentent les gradients desdites données scalaires bidimensionnelles, puis que le Laplacien estimé (Δφ_K(i,j)) soit calculée et soit comparé avec ladite fonction (f(i)) afin de déterminer si la différence entre ladite fonction et ledit Laplacien estimé (Δφ_K(i,j)) en chaque point arrive en deçà d'une valeur de seuil prédéterminée, et, si ce n'est pas le cas, effectuer des approximations identiques supplémentaires sur la base des valeurs corrigées jusqu'à ce que ladite différence (E_K) se trouve en deçà de ladite valeur de seuil.

12. Procédé de traitement de données scalaires selon la revendication 11, où, dans ladite opération (en 535) servant à reconstituer lesdites données scalaires bidimensionnelles, ladite valeur (Δφ_K(i,j)) du Laplacien en chaque point est exprimée sous la forme Δφ_K(i,j) = φ_K(i+1,j) + φ_K(i,j+1) + φ_K(i-1,j) + φ_K(i,j-1) - 4φ_K(i,j), où i est la coordonnée x, j est la coordonnée y, et K est le nombre d'approximations successives.

13. Procédé de traitement de données scalaires selon la revendication 11, où, dans ladite opération (en 535) servant à reconstituer lesdites données scalaires bidimensionnelles, ladite valeur (Δφ_K(i,j)) du Laplacien en chaque point est exprimée sous la forme Δφ_K(i,j) = 2φ_K(i,j) - 2φ_K(i-1,j) + φ_K(i-2,j) - 2φ_K(i,j-1) + φ_K(i,j-2), où i est la coordonnée x, j est la coordonnée y, et K est le nombre d'approximations successives.

14. Appareil permettant de traiter des données scalaires de signaux d'informations, comme par exemple des données de signaux d'images, par compression de données scalaires bidimensionnelles de signaux d'informations définies sur une surface bidimensionnelle ayant une direction horizontale (i) et une direction verticale (j) et par reconstitution desdites données scalaires bidimensionnelles de signaux d'informations sur la base desdites données comprimées, ledit appareil comprenant :

1) un moyen (51) servant à détecter des lignes frontières (11-1, 11-2) desdites données scalaires bidimensionnelles de signaux d'informations (φ(i,j)), lesdites lignes frontières (11-1, 11-2) étant détectées de telle manière qu'un changement de la valeur desdites données scalaires bidimensionnelles de signaux d'informations entre des points adjacents situés sur ladite surface bidimensionnelle soit plus grand qu'une valeur de seuil prédéterminée ;

2) un moyen (532) servant à découper un domaine (12) entre lesdites lignes frontières (11-1, 11-2) suivant une première ligne horizontale (17) ayant des intersections avec lesdites lignes frontières ;

3) un moyen (533) servant à déterminer une fonction (f(i)) au titre d'une approximation du Laplacien desdites données scalaires bidimensionnelles (φ(i,j)), calculé en chaque point dudit domaine découpé (12) suivant ladite ligne horizontale ;

4) un moyen (534) servant à comprimer lesdites données scalaires bidimensionnelles de signaux d'informations (φ(i,j)) en remplaçant lesdites données scalaires bidimensionnelles présentes en chacun desdits points suivant ladite ligne horizontale (17) par des données scalaires présentes à l'intersection (13-1, 13-2) de ladite ligne horizontale avec lesdites lignes frontières (11-1, 11-2), les données scalaires représentant des gradients entre lesdites données scalaires bidimensionnelles présentes sur lesdites lignes frontières et des points adjacents (14-1, 14-2) suivant ladite ligne horizontale, et ladite fonction (f(i));

5) un moyen permettant de répéter les opérations 2 à 4 suivant d'autres lignes horizontales parallèles à ladite première ligne horizontale (17); et

6) un moyen (535) servant à reconstituer lesdites données scalaires bidimensionnelles par interpolation desdites données scalaires bidimensionnelles sur la base desdites données scalaires présentes sur lesdites lignes frontières (11-1, 11-2), lesdites données scalaires représentant des gradients entre lesdites données scalaires bidimensionnelles présentes sur lesdites lignes frontières et des points adjacents (14-1, 14-2) suivant ladite ligne horizontale, et ladite fonction (f(i)) obtenue lors de ladite opération de compression.

Drawing